On the inequivalence of statistical ensembles

We investigate the relation between various statistical ensembles of finite systems. If ensembles differ at the level of fluctuations of the order parameter, we show that the equations of states can present major differences. A sufficient condition for this inequivalence to survive at the thermodynamical limit is worked out. If energy consists in a kinetic and a potential part, the microcanonical ensemble does not converge towards the canonical ensemble when the partial heat capacities per particle fulfill the relation $c_{k}^{-1}+c_{p}^{-1}<0$.Comment: 4 pages, 4 figure

Effect of angular momentum on equilibrium properties of a self-gravitating system

The microcanonical properties of a two dimensional system of N classical particles interacting via a smoothed Newtonian potential as a function of the total energy E and the total angular momentum L are discussed. In order to estimate suitable observables a numerical method based on an importance sampling algorithm is presented. The entropy surface shows a negative specific heat region at fixed L for all L. Observables probing the average mass distribution are used to understand the link between thermostatistical properties and the spatial distribution of particles. In order to define a phase in non-extensive system we introduce a more general observable than the one proposed by Gross and Votyakov [Eur. Phys. J. B:15, 115 (2000)]: the sign of the largest eigenvalue of the entropy surface curvature. At large E the gravitational system is in a homogeneous gas phase. At low E there are several collapse phases; at L=0 there is a single cluster phase and for L>0 there are several phases with 2 clusters. All these pure phases are separated by first order phase transition regions. The signal of critical behaviour emerges at different points of the parameter space (E,L). We also discuss the ensemble introduced in a recent pre-print by Klinko & Miller; this ensemble is the canonical analogue of the one at constant energy and constant angular momentum. We show that a huge loss of informations appears if we treat the system as a function of intensive parameters: besides the known non-equivalence at first order phase transitions, there exit in the microcanonical ensemble some values of the temperature and the angular velocity for which the corresponding canonical ensemble does not exist, i.e. the partition sum diverges.Comment: 17 pages, 11 figures, submitted to Phys. Rev.

Modeling of demagnetization processes in permanent magnets measured in closed-circuit geometry

International audienceThe hysteresis loops of nucleation-type magnets made of exchange-decoupled grains (i.e. sintered Nd-Fe-B magnets) reflect the discrete character of magnetization switching in such materials. Due to this discrete character, the experimental determination of coercivity depends on the measurement protocol. Finite element modelling allows to investigate how the pattern of reversed grains develops during sample demagnetization performed under closed-circuit conditions, provided that the basic features of the hysteresigraph are known. Numerical modelling provides a quantitative understanding of the collective effects which are very pronounced in the closed-circuit configuration and shows how they affect both the slope of the demagnetizing curve and the sample coercivity. With a grain coercive field standard deviation adjusted to 0.1 T, it is numerically found that the difference in coercivity between closed-and open-circuit configurations is 40 kA/m, in good agreement with previous experimental data

Closed-Circuit Versus Open-Circuit Characterization of Hard Magnets

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Revisiting the demagnetization curves of Dy-diffused Nd-Fe-B sintered magnets

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